Cosmos in Greece, and the question about China

Order and ornament

The Greek word kosmos meant something humbler than the sky. In Homer it is the right arrangement of a thing: troops drawn up in good order, or a woman’s dress and jewels. That is why English has both cosmos and cosmetics, which come from the same root, a verb meaning “to arrange” and “to adorn.” Sometime in the sixth and fifth centuries BCE, Greek thinkers began to use the word for the whole world, as if it too were a well-ordered, well-adorned thing. The philosopher Heraclitus, around 500 BCE, wrote that this kosmos was made by no god and no human being, and his is the earliest surviving use of the word in that sense. A later tradition credits Pythagoras with being the first to call the heavens a kosmos; our sources for that are centuries younger, and even they disagree about who deserves the credit.

This course gives the Greek cosmos three marks. A cosmos is harmonious, in that its parts are related by number and ratio. It is ordered, in that each part has its place. And it is a whole with a shape you could draw. The opposite is chaos, and it is common to say that the Greeks pictured the cosmos as growing out of chaos. That is not quite the old story. In Hesiod’s Theogony (around 700 BCE) Chaos is simply the first thing to come to be, and the word means a gap or gaping space, not a mess. The picture of order imposed on a jumbled mass comes later: from Plato, who has the maker of the world bring things from disorder into order, and from the Roman poet Ovid, who calls chaos “a rough, unarranged mass.”

In Lesson 1 we saw that to treat the universe as a thing is to run into paradox. The Greeks did it without worry. For them the world was a thing, with a shape and an order, and the mind could grasp it. This course argues that this was the Greek invention: to turn the whole into an object of thought.

Spheres and circles

The shape they gave it was a sphere. In the Timaeus Plato has the maker of the world choose a round shape, because the sphere is the most complete shape and the most like itself. Aristotle, in On the Heavens, gives more reasons. The circle is the first of the plane figures and the sphere the first of the solids; the sphere alone is bounded by a single surface; and a body of any other shape, turning, would need empty space around it to turn in. The older philosopher Parmenides had compared what is to “the bulk of a well-rounded sphere,” though that was about Being and not the sky.

Some modern accounts credit the Greeks with another reason: that of all solids with a given surface the sphere holds the most. It does, as the activity below lets you check. But that theorem is not in Plato or Aristotle. It was stated later, by the mathematician Zenodorus in the second century BCE, whose work survives only through later writers such as Theon and Pappus, and it was proved in full generality only in the 1800s. For the Greeks the sphere came first as a matter of perfection and symmetry; the argument from capacity was a later reason added to a belief already held.

The astronomers then had to make the wandering planets fit. A Pythagorean system, which Aristotle reports without naming its author and which later writers linked to Philolaus, put a central fire at the middle of the cosmos with the earth circling it, a fire we never see because the inhabited side of the earth faces away. (It is not a sun-centered system: the sun is one of the circling bodies.) Counting the sphere of the stars, the sun, the moon, the five planets and the earth gives nine bodies, and the Pythagoreans, for whom ten was the number of completeness, invented a tenth, a “counter-earth,” hidden on the far side of the fire. Aristotle was unimpressed: they were forcing the facts, he said, to fit their theories. Ten is not a “perfect number” in the mathematicians’ sense, which is a number equal to the sum of its divisors, like 6 or 28. For the Pythagoreans it meant complete.

Not long after, Eudoxus of Cnidus, around 360 BCE, tried the other way: to explain the planets’ looping paths using nothing but steady circular motion. His answer was a set of nested spheres, all centered on the earth. Each turns uniformly about its own axis and is carried by the one outside it. Combine two spheres turning in opposite directions on tilted axes and a planet traces a figure-eight curve, which reproduces its retrograde loop. In the standard reconstruction Eudoxus used 27 spheres; his follower Callippus brought the total to 34; and Aristotle, who turned the spheres into real transparent shells, needed 55. About five centuries later Ptolemy (about 150 CE) replaced the nested shells with a sharper mathematical device: a planet moves on a small circle, the epicycle, whose center moves on a larger circle, the deferent, with the earth near the middle. Later writers said that Plato had set astronomers the task of finding the steady circular motions that would “save the appearances.” Courses 3 and 4 tell this story at length, and Course 3 shows a working epicycle.

The loops these models explain are real. Mercury, for example, seems to move backward against the stars about three times a year, sometimes four, for about three weeks each time. It is an effect of our own motion, like a car you overtake that seems for a moment to slide backward. This course notes a deeper habit in all of it: explain a complicated motion by breaking it into simple circles and adding them back. It is the habit of analysis, and it is how engineers still decompose a sound into pure tones.

A cosmos shaped like a city

Why did the Greeks picture the world as a centered, symmetrical circle? One answer looks to their cities. A Greek city-state, the polis, had an open public square at its center, the agora, where citizens gathered, and in a democracy like Athens, from 508 BCE, citizens met to speak and vote. Greek theaters curve around a round floor so that every seat looks to the same middle. The circle is the shape of equals: every point on it is the same distance from the center. In this reading the political circle became the cosmic one.

This is a real scholarly thesis, argued by the French historian Jean-Pierre Vernant in The Origins of Greek Thought (1962), building on an essay of 1947 by Gregory Vlastos. Its best evidence is the philosopher Anaximander of Miletus (about 610–546 BCE), who said that the earth hangs unsupported at the center of the cosmos and stays there because it is equally far from everything. Aristotle, who reports this, calls it ingenious, but not true. Vernant saw in that reasoning, no center of the world more entitled to the earth than any other direction, an echo of the equality of citizens in a city.

It remains a thesis. Another scholar, Robert Hahn, argues that Anaximander’s model came from the technology of architects, such as column drums and simple ratios, not from politics; and Carol Atack points out that the comparison between divine and civic order is older than the polis. The tidy picture also fails on the facts of the Greek world: Sparta had two hereditary kings, many cities were ruled by oligarchs or tyrants, and Greek astronomy at its mathematical peak, from Aristarchus to Ptolemy, flourished under the Hellenistic kings and Roman rule, with Alexandria at its center. The thesis is worth keeping as an example of the kind of explanation this course likes: ideas about the cosmos are shaped by how people live, and not by observation alone.

Did China have a cosmos?

Here this course makes its boldest claim, and, because it is bold, we have to be careful with it. The claim in its strongest form is that ancient China had astronomy and calendars, but no cosmology in the Greek sense: no worked-out picture of the shape and structure of the whole, built up and argued over. Chinese thinkers, it says, were skeptical about the largest questions, content to raise them and leave them. Its evidence is of four kinds, and each is real, and each, as we shall see, needs qualifying.

First, the word. 宇宙 (yǔzhòu), the Chinese word for the universe, meant in the classics a frame of space and time. The Shizi says 宇 is the four directions and up and down, and 宙 is the past and the present; the Huainanzi (about 139 BCE) adds that the Way lies between them and no one knows where. A frame is not a thing with a shape. Second, the great poem Tian wen (“Heavenly Questions”), attributed to Qu Yuan (about 300 BCE), asks who could have known how the world began, how the nine layers of heaven were measured, where the pivot of heaven is tied, and what holds up the eight pillars, and it gives no answers. Third, the story of the man of Qi, in the Liezi, who was so afraid heaven and earth would fall that he could not eat or sleep. In the story’s ending the sage Liezi says that both “they will fall” and “they will not fall” are mistakes, since falling or not falling is something he cannot know. That is agnosticism, stated outright. Fourth, the three models of the sky.

Gai tian (盖天), the “covering heaven,” is quoted in the official history Jin shu (648 CE) as the view of the Zhou bi school: “heaven is round like a spread-out umbrella, earth is square like a chessboard.” Hun tian (浑天), the “spherical heaven,” likens the sky to a hen’s egg and the earth to the yolk, with the sky large, the earth small, and water inside the shell. Xuan ye (宣夜) says the sun, moon and stars float in empty space, moved by qi. This course reads them as marginal and unfinished: gai tian does not fit the sky, hun tian is not the Greek sphere, and xuan ye is a lost book reduced to one paragraph.

Why Greece?

If the Greeks did invent the geometric cosmos, why them? This course mentions a few conditions: the Greeks lived near Egypt and Mesopotamia, old civilizations from which they could learn; and their land was poor, which sent them out to sea. The first is well supported: historians such as Walter Burkert have shown how much Greek culture owed to the Near East, which also makes the Greek story less a miracle. The second is the kind of explanation that is easy to give afterward, and we found no firm scholarly source for it. The historian of science Geoffrey Lloyd points to another factor: Greek thinkers argued in public, before assemblies and rival schools, and so had to defend a theory against rivals, while in China the state patronized scholars, which gave stability but, in his view, encouraged conservatism. “Why Greece?” remains an open question, and so does its twin, the Needham question, why modern science arose in Europe and not China, which you met in Course 2.